EDP Sciences logo
Subscriber Authentication Point
Search
Menu
Home All issues Volume 550 (February 2013) A&A, 550 (2013) A47 Full HTML
Free Access
Issue
A&A
Volume 550, February 2013
Article Number A47
Number of page(s) 6
Section The Sun
DOI https://doi.org/10.1051/0004-6361/201220103
Published online 23 January 2013

© ESO, 2013

1. Introduction

The study of the interaction between waves and magnetic fields plays an important role in the investigation of the mechanisms responsible for solar corona heating. It is well established that the amplitude of solar five-minute oscillations in the photosphere is reduced by a factor of two to three within active regions (ARs; Leighton et al. 1962; Woods & Cram 1981; Lites et al. 1982; Abdelatif et al. 1986; Braun et al. 1987; Tarbell et al. 1988; Braun et al. 1988; Title et al. 1992; Hindman & Brown 1998). The reduction is observed to depend on frequency, depth, and on the physical parameters that describe the flux tubes, i.e., their radius and magnetic strength (Brown et al. 1992; Hindman & Brown 1998; Gordovskyy & Jain 2008). In addition, this behavior has been found in small magnetic field concentrations (Roberts & Webb 1978; Spruit 1981; Bogdan et al. 1996; Cally & Bogdan 1997; Hindman & Jain 2008, 2012; Jain et al. 2009; Pradeep Chitta et al. 2012).

It is also known that at higher frequencies, above the acoustic cutoff frequency in the low photosphere, the velocity oscillation amplitude is enhanced at the edges of ARs (Braun et al. 1992; Brown et al. 1992; Toner & Labonte 1993). Furthermore, an enhancement of power in the three-minute band has recently been observed in the inner umbra of a pore (Stangalini et al. 2012).

Several mechanisms have been proposed to explain the observations (Hindman et al. 1997):

  • 1)

    Intrinsic power inhibition due to local convection suppression.By using numerical simulations, Parchevsky &Kosovichev (2007) found that the reduction ofwave excitation in a sunspot can account for up to 50% of the power deficit.

  • 2)

    Partial p-mode absorption (Braun et al. 1987; Bogdan et al. 1993; Cally 1995; Cally & Andries 2010). Spruit & Bogdan (1992) showed that wave absorption by sunspots can be interpreted in terms of p-mode conversion between the oscillations and magnetohydrodynamics (MHD) waves. Both models (Cally & Bogdan 1993) and simulations (Cameron et al. 2008) have shown that mode conversion is able to remove a significant amount of energy from the incident helioseismic wave with an efficiency that depends on the angle of the magnetic field from the vertical, with a maximum at about 30° (Cally et al. 2003; Crouch & Cally 2003).

  • 3)

    Opacity effects. Within a magnetic region, the line-of-sight optical depth experiences a depression (Wilson depression). Due to increasing density, the amplitude of the velocity fluctuations decreases with depth.

  • 4)

    Alteration of the p-mode eigenfunctions by the magnetic field (Jain et al. 1996; Hindman et al. 1997).

We note that the majority of studies on the interaction between solar oscillations and magnetic field have focused on the use of models and simulations.

Because of the dependence of velocity amplitude on magnetic strength, the most noticeable effects are observed within ARs, where the strongest magnetic fields are found. Among them, bipolar active regions (hereafter βARs) are particularly interesting, showing asymmetries in their morphology and physical properties, as several works have already pointed out (see, e.g., Bray & Loughhead 1979; Balthasar & Woehl 1980; Ternullo et al. 1981; Zwaan 1985; van Driel-Gesztelyi & Petrovay 1990; Petrovay et al. 1990; Fan et al. 1993). Moreno-Insertis et al. (1994) conclude that morphological asymmetries are due to the different inclination with which the polarities of βARs emerge.

Using simulations, Fan et al. (1993) have studied area asymmetries, predicting that at the same depth the leading polarity must have a strength about twice as large as the trailing polarity. This result, which is a consequence of Coriolis force action on the magnetic structure, is able to account for the trailing spot fragmentation, its lower flux magnitude, and its shorter lifetime.

Recently, Michelson Doppler Imager (MDI) observations of 138 bipolar magnetic regions have quantitatively shown that the areas of leading polarities are typically smaller than those of trailing polarities (Yamamoto 2012). This area asymmetry could be produced by the Coriolis force during a flux tube’s rising motion in the solar convection zone.

In this work, we investigated the velocity oscillation amplitude reduction by the magnetic field within βARs. We analyzed 12 βARs from SDO-HMI (Helioseismic and Magnetic Imager) data, both in the northern (N) and southern (S) hemispheres, and found that the leading polarity systematically has a greater reduction in amplitude than the trailing. In addition, we studied the amplitude reduction as a function of the field inclination for AR11166.

2. SDO-HMI data

Our dataset consists of 12 SDO-HMI magnetograms and dopplergrams pairs with 1 arcsec spatial resolution (Scherrer et al. 2012; Schou et al. 2012). These were acquired with a 45-s cadence, which set the Nyquist frequency. Each βAR dataset is three hours long, which set the lower cut-off at  ~10-4   s-1. Observation times covered the interval from 2011 March 8 to 2012 January 3 (see Table 1).

We selected eight isolated bipolar regions in the N hemisphere and four in the S hemisphere. In order to limit the effects due to the inclination with respect to the line of sight, we selected βARs as close as possible to the disk center. The rectangular area enclosing the βARs was selected such that it included all magnetic features with strength above 500 G, with the the minimum and maximum allowed dimensions of the enclosing rectangle being 500 and 700 arcsec, respectively. Figure 1 shows the mean magnetograms of two selected βARs: AR 11166 in the N hemisphere and AR 11316 in the S hemisphere. In both panels, the leading polarity is on the right and is negative for the N βARs, positive for the S βARs. Table 1 shows the list of βARs analyzed in this work.

thumbnail Fig. 1

SDO-HMI mean magnetograms of a) AR 11166 b) AR 11316. See Table 1 for more details.

3. Method and analysis

The selected regions around each βAR were co-registered using a fast Fourier transform (FFT) technique that ensures sub-pixel accuracy. Inspection of the co-registered data shows that the strong magnetic structures remain in the same position during the entire duration of the acquisition. The amplitude of velocity oscillations was estimated pixel by pixel through their integrated spectrum. Specifically, we selected a spectral window Δν centered at 3 mHz (five-minute band) with a width of 1 mHz and then integrated the FFT amplitude spectrum Aν in that frequency range:

We then divided the data into bins of magnetic field, each 25 G wide, and averaged the amplitude of velocity oscillations in each bin, thus obtaining AB =  ⟨ Axy ⟩ B. We consider only pixels with |B| > 25 G. Since all the amplitude distributions within the respective magnetic bin have a Gaussian-like shape (see inset in Fig. 2b), we use as error on AB, where σ is the standard deviation and n are the counts in each bin.

4. Results and discussion

4.1. Oscillation amplitude vs. magnetic field strength

thumbnail Fig. 2

In panel a) the integrated velocity oscillation amplitude for AR11166 is shown; the same for AR1136 in panel b). The red overplots correspond to the average in each magnetic field bin. In the inset of panel b), amplitude distribution in the 25 < B < 50 G bin (black line) and Gaussian fit (red line) are shown.

In Fig. 2 we show the integrated amplitude Axy scatter plot (black dots) and AB for each magnetic bin (red line) for the βARs shown in Fig. 1. Hereafter, we refer to the AB plot as the amplitude profile. The amplitude shows a decreasing trend up to a plateau, which is almost always reached in the range 0.5−1 kG (as in the case of Fig. 2b). This feature suggests that the amplitude is independent of the magnetic field strength above a threshold value, which is different for each βAR and each polarity in the same βAR.

For every polarity present in the 12 βARs analyzed, we computed the oscillation amplitude reduction as the ratio d = A1000/A25, where A1000 and A25 are, respectively, the mean oscillation velocity around B = 1000 G, and B = 25 G, the minimum observable strength. Averaging the d values over all the βARs, we obtained , which agrees with the oscillation amplitude reductions in magnetic environments quoted in the literature (e.g., Woods & Cram 1981; Lites et al. 1982; Braun et al. 1987; Tarbell et al. 1988).

The plateau in the amplitude profiles for high B values is intriguing. By visual inspection, we verified that it takes place almost exclusively in the βAR spot umbrae, as can be expected, given the high magnetic field values. We can exclude an instrumental effect, since the magnetic strength threshold changes with each βAR and even with the polarity in the same βAR, and we are well above the 20 m s-1 error on the velocity measurements due to the HMI filter transmission profiles (Fleck et al. 2011). It seems that the oscillation amplitudes are not completely suppressed, even in the strongest magnetic fields, and are not dependent on the magnetic field strength anymore. In contrast to the simulations of Cattaneo et al. (2003), it may indicate a saturation effect of the kinetic energy in the strong field regime and shed new light on the mechanisms that co-operate in the reduction of acoustic power in the lower atmosphere.

Table 1

Details of SDO-HMI data used.

4.2. The leading-trailing asymmetry

To investigate the relations between local oscillation amplitude and magnetic field strength, we compute the midpoints of the amplitude profiles. Specifically, we draw horizontal lines at constant AB values, proceeding down in steps of 10 m s-1. We compute the abscissa of each midpoint on the segment that intersects the amplitude profiles. If these profiles were symmetric, the midpoints should be on the B = 0 vertical line. In order to compare the amplitude profiles from different βARs, we normalize them to their average value AB in the B =  ±25 G bins. For solar cycle 24, the leading polarities are negative in the N hemisphere and positive in the S hemisphere. Figure 3a shows the midpoint lines for all the 12 βARs considered in this study. Northern and southern βAR families appear well defined and separated. Moreover, as can be seen in Fig. 3, the amount of asymmetry, defined as the distance of each midpoint from the vertical line through B = 0, increases for stronger fields. In the N hemisphere (in blue), it extends up to |B| ≃ 230 G, while in S hemisphere (in red), it is less apparent, and only reaches |B| ≃ 130 G. The amplitude profiles of N βARs are biased toward positive polarities, i.e., the trailing, while the S βARs are biased toward negative polarities, i.e., the trailing again.

thumbnail Fig. 3

a) Midpoints for normalized velocity oscillation amplitude. b) Difference between oscillation amplitude for both polarities against the magnetic strength. Bars represent errors. Red line with diamonds refers to S βARs, blue line with plus signs to N βARs.

To visualize the asymmetry differently, we can fix a value |B| for the magnetic strength and compute the amplitude difference, i.e., the difference between the respective averaged amplitudes for both polarities in each βAR, namely, A|B| − A−|B|. In Fig. 3b, we show these differences vs the absolute value of magnetic strength for all βARs of Table 1. This plot confirms that the asymmetry is lower where the field is weaker. At 25 G the difference is about 10 m s-1 and typical values for velocity amplitudes up to 600 m s-1; at 1000 G the difference rises to over 50 m s-1, while the amplitudes are  ~200 m s-1. Both in N and S hemispheres, the oscillation amplitude in the trailing polarity is higher than that in the leading polarity. This fact implies that A|B| > A−|B| in the N hemisphere and vice versa in the S hemisphere, and that the amplitude reduction is less efficient in the trailing polarity.

Such an asymmetry suggests that the amount of oscillation reduction within magnetic environments is not a function of the local magnetic field strength only. If this were the case, we would observe the same oscillation amplitudes for B and −B magnetic fields. This would imply that both plots of Fig. 3 lie on the line through 0 G (a) and 0 m s-1 (b), respectively.

The simulations of Fan et al. (1993) about area asymmetries of βARs predicted a pronounced difference in field strength between the leading and the trailing polarities, as well as ensuing differences in their fragmentation and lifetimes. This suggests that the asymmetry we found could be derived from nonlocal properties, i.e., on the whole magnetic environment topology and even its surroundings.

We therefore computed the area asymmetry in our magnetograms following Yamamoto (2012), with a threshold B > 500 G. The results are reported in the fourth column of Table 1. We found that, on average, the area of the leading polarity is  ~90% of the trailing polarity area, regardless of the hemisphere which the βAR belongs to. This quantifies how much a trailing polarity is spread with respect to its leading polarity. We can speculate that a relation may exist between the area and the oscillation suppression due to a different interaction of acoustic waves with sparser or denser active region polarities.

4.3. Oscillation amplitude vs. magnetic field inclination The case of AR11166

To support the findings reported in Sect. 4.2, we studied the dependence of oscillation amplitude on the magnetic field inclination angle θ in an βAR. For this purpose, we considered the AR11166 (Fig. 1a) as a case study. We used the line-of-sight (LOS) inclination maps provided by the VFISV (Very Fast Inversion of the Stokes Vector, Borrero et al. 2011) inversion of HMI vector magnetic field data.

thumbnail Fig. 4

Inclination map of AR 11166. The leading polarity (negative) ranges from 90° to 180° and the trailing polarity (positive) from 0° to 90°.

In Fig. 4 we show the magnetic field inclination map of AR11166. The inclinations retrieved by the VFISV span the range 10° < θ < 172°. Following the most-used sign convention, the leading polarity (negative) ranges from 90° to 180° and the trailing polarity (positive) from 0° to 90°. As expected, the innermost umbrae are mostly line of sight, as the βARs were selected as close as possible to the disk center.

VFISV also provides the error σθ associated to the inclination for each pixel (Borrero et al. 2011; Press et al. 1986). To avoid polarity flips due to the inversion error, we discarded all those pixels where θ ± 3σθ causes the field to flip its inclination from positive to negative (or vice versa). We stress that VFISV is a Milne-Eddington code and is therefore blind to any B and v LOS gradients, which produce asymmetries in the Stokes profiles. This happens most often in regions filled by weak fields (Viticchié et al. 2011; Viticchié & Sánchez Almeida 2011). Moreover, the inversion of low signal-to-noise Stokes profiles is usually problematic (see Landi Degl’Innocenti 1992; Borrero et al. 2011, for more details). For noisy Stokes profiles and therefore low B values, VFISV (and any inversion code) tends to be biased toward  ~90° inclinations (Borrero & Kobel 2011). For these reasons and for consistency with the threshold used in Sect. 3, we rejected the pixels with B < 25 G and 75° < θ < 105°. After this selection, about 17% of the initial pixels were selected for the analysis.

We plotted Axy and its average in each θ bin Aθ =  ⟨ Axy ⟩ θ against the magnetic field inclination θ (shown in Fig. 5).

thumbnail Fig. 5

Integrated velocity oscillation amplitude within AR11166 as a function of the magnetic field inclination θ. The thick red line corresponds to the average amplitude Aθ =  ⟨ Axy ⟩ θ in each θ bin (Δθ = 1°). The vertical dashed lines mark the threshold θ < 75° OR θ > 105°.

For ease of comparison, in the upper panel of Fig. 6 we show again Aθ versus θ in the range  [10°,75°] .

thumbnail Fig. 6

Upper panel: and versus θ in the range  [10°,75°] . The blue line represents the average amplitude of the positive (trailing) polarity . The red line represents the average amplitude of the negative (leading) polarity after a remapping operation (θ → 180° − θ: ). Lower panel: ΔA versus θ (see the text). Vertical bars represent the errors, which were computed for each Aθ with the same method described in Sect. 3 and then summed up.

Both Aθ smoothly decrease from  ≃250 m s-1 to  ~140 m s-1, from almost horizontal to almost vertical fields, respectively, but the oscillation amplitude reduction is more effective for the leading polarity (red curve) than for the trailing polarity (blue curve).

In the lower panel of Fig. 6 we plot the oscillation amplitude asymmetry VS θ. Within the errors up to θ ≃ 45° ΔA is constant (≃15 m s-1), but then drops to very few m s-1.

The inclination analysis shows that a  ≃15 m s-1 asymmetry exists between the polarities of AR11166. In particular, the velocity oscillation amplitude is enhanced in the trailing polarity with respect to the leading polarity.

There is no evident relation between the asymmetry ΔA and the inclination θ. For any θ ≲ 45° the oscillation amplitude asymmetry is positive and around 15 m s-1. We interpret the drop at  ≃45° as the combined effect of the VFISV preference to associate weak fields with larger inclinations (Borrero & Kobel 2011) and the amplitude difference, which is small for weak fields (see Fig. 3b). Also, an incorrectly retrieved weak B may result from unresolved magnetic structuring in the pixel (e.g., Sánchez Almeida 1998; Socas-Navarro & Sánchez Almeida 2003; Viticchié et al. 2011), and we recall that a VFISV hypothesis is that the magnetic field is constant within the pixel.

Schunker & Cally (2006) and Stangalini et al. (2011) have demonstrated that, due to mode conversion, there exists a preferred angle at which the power is significant larger. In our case, we focus on the amplitude asymmetry between the two polarities instead of considering the proper amplitude dependence, which may be affected by biases due to the magnetic field strength.

5. Conclusions

In this work, we focused on the velocity oscillation amplitude reduction in βARs, reaching the following conclusions. The oscillation amplitude reduction found in magnetic environments of βARs is 0.54 ± 0.06, which agrees with the values quoted in the literature (e.g. Woods & Cram 1981; Lites et al. 1982; Braun et al. 1987; Tarbell et al. 1988). In addition, the five-minute amplitudes are not completely suppressed in the strongest magnetic fields of the spots’ innermost umbra. It would be very important to understand why a plateau appears in the oscillation amplitude profiles for strong fields.

There exists a leading-trailing polarity asymmetry in βARs. The asymmetry suggests that the reduction in oscillation amplitude does not depend on the field strength only, but also depends on nonlocal conditions, such as the area on which the field spreads. Furthermore, the trailing polarity systematically shows a higher oscillation amplitude than the leading polarity, regardless of the hemisphere which the βAR belongs to.

The plot of the velocity oscillation amplitude as a function of the magnetic field inclination confirms such an asymmetry in βARs. Apparently, the asymmetry does not depend on the inclination.

We used HMI full-disk data at a 45 s time cadence and at 1 arcsec spatial resolution. An analysis of these data revealed a possible saturation of the oscillation amplitude reduction for strong B and an asymmetry in such a reduction for leading-trailing polarities. These results have to be accounted for in modeling the power reduction in magnetic environments, as well as in the emergence and the evolution of βARs.

Acknowledgments

We thank Prof. Stuart M. Jefferies (IfA, University of Hawaii) for the useful discussion and critical reading of the early version of this manuscript. SDO-HMI data are courtesy of the NASA/SDO HMI science team. We acknowledge the VSO project (http://vso.nso.edu) through which data were easily obtained.

References

  1. Abdelatif, T. E., Lites, B. W., & Thomas, J. H. 1986, ApJ, 311, 1015 [NASA ADS] [CrossRef] [Google Scholar]
  2. Balthasar, H., & Woehl, H. 1980, A&A, 92, 111 [NASA ADS] [Google Scholar]
  3. Bogdan, T. J., Brown, T. M., Lites, B. W., & Thomas, J. H. 1993, ApJ, 406, 723 [NASA ADS] [CrossRef] [Google Scholar]
  4. Bogdan, T. J., Hindman, B. W., Cally, P. S., & Charbonneau, P. 1996, ApJ, 465, 406 [NASA ADS] [CrossRef] [Google Scholar]
  5. Borrero, J. M., & Kobel, P. 2011, A&A, 527, A29 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  6. Borrero, J., Tomczyk, S., Kubo, M., et al. 2011, Sol. Phys., 273, 267 [Google Scholar]
  7. Braun, D. C., Duvall, Jr., T. L., & Labonte, B. J. 1987, ApJ, 319, 27 [Google Scholar]
  8. Braun, D. C., Duvall, Jr., T. L., & Labonte, B. J. 1988, ApJ, 335, 1015 [NASA ADS] [CrossRef] [Google Scholar]
  9. Braun, D. C., Lindsey, C., Fan, Y., & Jefferies, S. M. 1992, ApJ, 392, 739 [Google Scholar]
  10. Bray, R. J., & Loughhead, R. E. 1979, Sunspots [Google Scholar]
  11. Brown, T. M., Bogdan, T. J., Lites, B. W., & Thomas, J. H. 1992, ApJ, 394, L65 [NASA ADS] [CrossRef] [Google Scholar]
  12. Cally, P. S. 1995, ApJ, 451, 372 [NASA ADS] [CrossRef] [Google Scholar]
  13. Cally, P. S., & Andries, J. 2010, Sol. Phys., 266, 17 [NASA ADS] [CrossRef] [Google Scholar]
  14. Cally, P. S., & Bogdan, T. J. 1993, ApJ, 402, 721 [NASA ADS] [CrossRef] [Google Scholar]
  15. Cally, P. S., & Bogdan, T. J. 1997, ApJ, 486, 67 [Google Scholar]
  16. Cally, P. S., Crouch, A. D., & Braun, D. C. 2003, MNRAS, 346, 381 [NASA ADS] [CrossRef] [Google Scholar]
  17. Cameron, R., Gizon, L., & Duvall, Jr., T. L. 2008, Sol. Phys., 251, 291 [NASA ADS] [CrossRef] [Google Scholar]
  18. Cattaneo, F., Emonet, T., & Weiss, N. 2003, ApJ, 588, 1183 [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  19. Crouch, A. D., & Cally, P. S. 2003, Sol. Phys., 214, 201 [NASA ADS] [CrossRef] [Google Scholar]
  20. Fan, Y., Fisher, G. H., & Deluca, E. E. 1993, ApJ, 405, 390 [Google Scholar]
  21. Fleck, B., Couvidat, S., & Straus, T. 2011, Sol. Phys., 271, 27 [NASA ADS] [CrossRef] [Google Scholar]
  22. Gordovskyy, M., & Jain, R. 2008, ApJ, 681, 664 [NASA ADS] [CrossRef] [Google Scholar]
  23. Hindman, B. W., & Brown, T. M. 1998, ApJ, 504, 1029 [NASA ADS] [CrossRef] [Google Scholar]
  24. Hindman, B. W., & Jain, R. 2008, ApJ, 677, 769 [NASA ADS] [CrossRef] [Google Scholar]
  25. Hindman, B. W., & Jain, R. 2012, ApJ, 746, 66 [NASA ADS] [CrossRef] [Google Scholar]
  26. Hindman, B. W., Jain, R., & Zweibel, E. G. 1997, ApJ, 476, 392 [NASA ADS] [CrossRef] [Google Scholar]
  27. Jain, R., Hindman, B. W., & Zweibel, E. G. 1996, ApJ, 464, 476 [NASA ADS] [CrossRef] [Google Scholar]
  28. Jain, R., Hindman, B. W., Braun, D. C., & Birch, A. C. 2009, ApJ, 695, 325 [NASA ADS] [CrossRef] [Google Scholar]
  29. Landi Degl’Innocenti, E. 1992, Magnetic field measurements, eds. F. Sanchez, M. Collados, & M. Vazquez, 71 [Google Scholar]
  30. Leighton, R. B., Noyes, R. W., & Simon, G. W. 1962, ApJ, 135, 474 [NASA ADS] [CrossRef] [Google Scholar]
  31. Lites, B. W., White, O. R., & Packman, D. 1982, ApJ, 253, 386 [NASA ADS] [CrossRef] [Google Scholar]
  32. Moreno-Insertis, F., Caligari, P., & Schuessler, M. 1994, Sol. Phys., 153, 449 [NASA ADS] [CrossRef] [Google Scholar]
  33. Parchevsky, K. V., & Kosovichev, A. G. 2007, ApJ, 666, L53 [NASA ADS] [CrossRef] [Google Scholar]
  34. Petrovay, K., Marik, M., Brown, J. C., Fletcher, L., & van Driel-Gesztelyi, L. 1990, Sol. Phys., 127, 51 [NASA ADS] [CrossRef] [Google Scholar]
  35. PradeepChitta, L., Jain, R., Kariyappa, R., & Jefferies, S. M. 2012, ApJ, 744, 98 [NASA ADS] [CrossRef] [Google Scholar]
  36. Press, W. H., Flannery, B. P., & Teukolsky, S. A. 1986, Numerical recipes The art of scientific computing [Google Scholar]
  37. Roberts, B., & Webb, A. R. 1978, Sol. Phys., 56, 5 [NASA ADS] [CrossRef] [Google Scholar]
  38. Sánchez Almeida, J. 1998, in Three-Dimensional Structure of Solar Active Regions, eds. C. E. Alissandrakis, & B. Schmieder, ASP Conf. Ser., 155, 54 [Google Scholar]
  39. Scherrer, P., Schou, J., Bush, R., et al. 2012, Sol. Phys., 275, 207 [Google Scholar]
  40. Schou, J., Scherrer, P., Bush, R., et al. 2012, Sol. Phys., 275, 229 [Google Scholar]
  41. Schunker, H., & Cally, P. S. 2006, MNRAS, 372, 551 [NASA ADS] [CrossRef] [Google Scholar]
  42. Socas-Navarro, H., & Sánchez Almeida, J. 2003, ApJ, 593, 581 [NASA ADS] [CrossRef] [Google Scholar]
  43. Spruit, H. C. 1981, A&A, 98, 155 [NASA ADS] [Google Scholar]
  44. Spruit, H. C., & Bogdan, T. J. 1992, ApJ, 391, 109 [Google Scholar]
  45. Stangalini, M., Del Moro, D., Berrilli, F., & Jefferies, S. M. 2011, A&A, 534, A65 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  46. Stangalini, M., Giannattasio, F., Del Moro, D., & Berrilli, F. 2012, A&A, 539, L4 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  47. Tarbell, T. D., Peri, M., Frank, Z., Shine, R., & Title, A. M. 1988, in ESA Spec. Publ. 286, Seismology of the Sun and Sun-Like Stars, ed. E. J. Rolfe, 315 [Google Scholar]
  48. Ternullo, M., Zappala, R. A., & Zuccarello, F. 1981, Sol. Phys., 74, 111 [NASA ADS] [CrossRef] [Google Scholar]
  49. Title, A. M., Topka, K. P., Tarbell, T. D., et al. 1992, ApJ, 393, 782 [NASA ADS] [CrossRef] [Google Scholar]
  50. Toner, C. G., & Labonte, B. J. 1993, ApJ, 415, 847 [NASA ADS] [CrossRef] [Google Scholar]
  51. van Driel-Gesztelyi, L., & Petrovay, K. 1990, Sol. Phys., 126, 285 [NASA ADS] [CrossRef] [Google Scholar]
  52. Viticchié, B., & Sánchez Almeida, J. 2011, A&A, 530, A14 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  53. Viticchié, B., Sánchez Almeida, J., Del Moro, D., & Berrilli, F. 2011, A&A, 526, A60 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  54. Woods, D. T., & Cram, L. E. 1981, Sol. Phys., 69, 233 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  55. Yamamoto, T. T. 2012, A&A, 539, A13 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  56. Zwaan, C. 1985, Sol. Phys., 100, 397 [NASA ADS] [CrossRef] [Google Scholar]

All Tables

Table 1

Details of SDO-HMI data used.

In the text

All Figures

thumbnail Fig. 1

SDO-HMI mean magnetograms of a) AR 11166 b) AR 11316. See Table 1 for more details.
In the text
thumbnail Fig. 2

In panel a) the integrated velocity oscillation amplitude for AR11166 is shown; the same for AR1136 in panel b). The red overplots correspond to the average in each magnetic field bin. In the inset of panel b), amplitude distribution in the 25 < B < 50 G bin (black line) and Gaussian fit (red line) are shown.
In the text
thumbnail Fig. 3

a) Midpoints for normalized velocity oscillation amplitude. b) Difference between oscillation amplitude for both polarities against the magnetic strength. Bars represent errors. Red line with diamonds refers to S βARs, blue line with plus signs to N βARs.
In the text
thumbnail Fig. 4

Inclination map of AR 11166. The leading polarity (negative) ranges from 90° to 180° and the trailing polarity (positive) from 0° to 90°.
In the text
thumbnail Fig. 5

Integrated velocity oscillation amplitude within AR11166 as a function of the magnetic field inclination θ. The thick red line corresponds to the average amplitude Aθ =  ⟨ Axy ⟩ θ in each θ bin (Δθ = 1°). The vertical dashed lines mark the threshold θ < 75° OR θ > 105°.
In the text
thumbnail Fig. 6

Upper panel: and versus θ in the range  [10°,75°] . The blue line represents the average amplitude of the positive (trailing) polarity . The red line represents the average amplitude of the negative (leading) polarity after a remapping operation (θ → 180° − θ: ). Lower panel: ΔA versus θ (see the text). Vertical bars represent the errors, which were computed for each Aθ with the same method described in Sect. 3 and then summed up.
In the text

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.